Fractal structure of lunar topography: An interpretation of topographic characteristics

Cao, Wei; Cai, Zhanchuan; Tang, Zesheng

doi:10.1016/j.geomorph.2015.03.002

Cited by 14 publications

(10 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Investigation of the fractal properties of relief (Figure 3) indicated that about 3% of the spatial units do not exhibit scaling behavior. This result is not surprising, since the fractal model does not necessarily work for every portion and type of landscape (Klinkenberg and Goodchild, 1992;Cao et al, 2015). These units are mainly located in correspondence with Lake Trasimeno, and along the main valleys and flat areas.…”

Section: Discussionmentioning

confidence: 96%

“…When the study aims at investigating the scaling properties of landscape surfaces, different techniques may be applied. The box-counting method was used, for example, to investigate the relationship between the elevation of relief and its fractal dimension (Cheng et al, 1999), and in cosmological studies for the interpretation of lunar topography (Cao et al, 2015). The triangular prism method was introduced by Clarke (1986) as an adaptation of the walking compass method (Mandelbrot, 1967) to two-and threedimensional surfaces, and it was used in a variety of studies (e.g., Ramish et al, 2012;Frattini and Crosta, 2013).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

Liucci

Melelli

2017

Earth Surf Processes Landf

View full text Add to dashboard Cite

Landscape topography widely exhibits fractal structure. Because of the complexity of relief geometry this structure is not homogeneous in space, and the study of its spatial characteristics represents a powerful method for investigating the interrelationships between landforms and underlying processes. We explore these interrelationships using the digital elevation model (DEM) of an area located in central Italy, where landscape topography is strongly linked to its geological evolution, being characterized by alternating intermountain basins and mountain ranges trending NW–SE. A modified version of the method based on the standard deviation of relief elevations is used to evaluate the fractal parameters of relief after tiling the DEM in spatial units characterized by homogeneous fractal geometry, and statistical methods in conjunction with spatial analysis techniques are applied to the resulting terrain datasets. Both the lowest and (to a lesser extent) the highest values of fractal dimension are found to follow the ridge‐and‐valley trend. Low fractal dimension is observed in the mountain ranges characterized by massive strata of limestone, and along the fault scarps defining the contact between the intermountain basins and the surrounding slopes, where sediment deposition prevails. High fractal dimension is observed in regions characterized by highly erodible terrigenous lithology, and in areas where tectonic activity favors erosional processes mainly by rivers. The analysis of the (fractal) power law parameters also suggests that each major lithological complex has its own characteristic fractal signature. These results provide new insights into the link between the fractal properties of topography and the tectonic, lithological, and geomorphological features of the area, and show that the analysis approach proposed is useful to depict key aspects about the geomorphological and geological setting of an area, using only a DEM. Copyright © 2017 John Wiley & Sons, Ltd.

show abstract

Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

Liucci

Melelli

2017

Earth Surf Processes Landf

View full text Add to dashboard Cite

show abstract

“…Because these topographic analyses were performed based on the merged DEM and the resolutions of the produced slope map was~59-and~30-m scale. According to the previous studies, the lunar topographic textures (such as slope, roughness, and entropy values) show scale dependence (Cao et al, 2015;Kreslavsky et al, 2013;Li, Wang, et al, 2016;Robbins, 2018). Kreslavsky et al (2013) found that hectometer-scale lunar roughness poorly correlated with kilometer-scale lunar roughness, because they reflected different sets of geologic processes and time scales.…”

Section: 1029/2018ea000507mentioning

confidence: 96%

High‐Resolution Terrain Analysis for Lander Safety Landing and Rover Path Planning Based on Lunar Reconnaissance Orbiter Narrow Angle Camera Images: A Case Study of China's Chang'e‐4 Probe

Yue

Zhang

et al. 2019

Earth and Space Science

View full text Add to dashboard Cite

China's Chang'e‐4 (CE‐4) probe will explore the South Pole‐Aitken basin in late 2018. Its preselected landing area is located on the southeastern floor of the Von Kármán crater. Landing experience of China's Chang'e‐3 probe may not be applied to CE‐4 mission directly because the topography of lunar farside is more rugged. Moreover, due to scale dependence and smooth effects, the previous topographic studies derived from digital elevation model data with lower resolution cannot represent the meter‐scale topographic features. Because of low time and space complexities in lunar images, image segmentation algorithm is especially suitable for recognizing lunar features. We divided the narrow angle camera (NAC) mosaic image into three parts: dark area, bright area, and flat area, based on a double‐threshold Otsu method. The first two parts corresponded to the undulating areas (positive and negative terrains). And then we calculated the flat area percentage (Fap) of the previous successful lunar landing missions (including Chang'e‐3, Apollo, Surveyor, and Luna series) and obtained the Fap threshold (>0.6) for lunar safe landing. According to Fap map (~1.5 m per pixel) of CE‐4 preselected landing area, the divided square grids with a size of 0.01° can be classified into safe grids (Fap > 0.6) and unsafe grids (Fap ≤ 0.6). The CE‐4 preselected landing areas can be greatly reduced to five potential landing areas. In the last, we proposed a route planning method, which took both the distance and security into account, for CE‐4 rover to dynamically generate a safe and short route between current grid and target grid.

show abstract

“…They therefore suggest that the median differential slope method can be used to assess the stratigraphic age of a region. Cao et al (2015a) provided the second fractal-based roughness analysis of the lunar surface, following the calculation of the Hurst exponent by Rosenburg et al (2011). As noted by Cao et al (2015a) the calculation of the Hurst exponent by Rosenburg et al (2011) relied on the use of along-track LOLA data and therefore characterized only one-dimensional slopes.…”

Section: Introductionmentioning

confidence: 99%

“…Cao et al (2015a) provided the second fractal-based roughness analysis of the lunar surface, following the calculation of the Hurst exponent by Rosenburg et al (2011). As noted by Cao et al (2015a) the calculation of the Hurst exponent by Rosenburg et al (2011) relied on the use of along-track LOLA data and therefore characterized only one-dimensional slopes. Cao et al (2015a) used LOLA gridded data to calculate the twodimensional fractal dimension (FD) of the lunar surface at different baselines (moving windows of 0.25-2°).…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Topographic Roughness of the Moon Using the Wavelet Leaders Method and the Lunar Digital Elevation Model From the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera

2020

View full text Add to dashboard Cite

The Wavelet Leaders Method (WLM) is a wavelet-based multifractal formalism that allows the identification of scale breaks (thus scaling regimes), the definition of scaling properties (mono versus multi fractality of the surface), and the calculation of the Hölder exponent that characterizes each pixel, based on the comparison between a theoretical wavelet and topographic values. Here we use the WLM and the SLDEM2015 digital elevation model to provide a near-global and a local isotropic characterization of the lunar roughness. The near-global study of baselines between 330 m and 1,350 km reveals scale breaks at~1.3, 42.2, and 337.6 km. Scaling properties and Hölder exponent values were calculated for the three corresponding scaling regimes: 330-659 m, 1.3-21.1 km, and 42.2-168.8 km. We find that the dichotomy between the highlands and the maria is present at all scales. Between 330 and 659 m, the Hölder exponent map shows the unique signature of Orientale basin, rilles, and a correlation with the age of mare units. Between 1.3 and 21.1 km, it shows the unique signature of the Orientale basin and a relationship with the density of 5-to 20-km-diameter craters. Scaling properties and Hölder exponent values were also calculated locally for complex craters, basins, rilles and light plains, for two scaling regimes: 165-659 m and 1.3-21.1 km. Relationships between the Hölder exponent values at 165-659 m, the density of <500-m-diameter craters and different geologic units were found and a potential scale break near 165 m was identified.Plain Language Summary Measures of topographic roughness are important as they can be used to better understand the fundamental processes shaping planetary surfaces and map regional variations of texture or identify geomorphologic units. Here we use a new approach to characterize the roughness of the Moon, which involves the comparison of a theoretical wavelet to topographic measurements. From this comparison we can identify at which scales the topographic roughness changes in properties and quantify these properties. We find that the roughness has distinct characteristics in three scale ranges: 330-659 m, 1.3-21.1 km, and 42.2-168.8 km. For example, at scales lower than 659 m, mare basalt surfaces appear to become rougher with age as they contain more 330-to 659-m-diameter craters, whereas between 1.3 and 21.1 km, contiguous geological units exhibit different levels of roughness, which allows to delineate them. The new approach to characterize the surface roughness has successfully been applied and validated on the Moon and can thus be confidently used to better understand the processes shaping other less studied planetary surfaces and aid in their geologic mapping.

show abstract

Fractal structure of lunar topography: An interpretation of topographic characteristics

Cited by 14 publications

References 24 publications

The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

High‐Resolution Terrain Analysis for Lander Safety Landing and Rover Path Planning Based on Lunar Reconnaissance Orbiter Narrow Angle Camera Images: A Case Study of China's Chang'e‐4 Probe

Analysis of the Topographic Roughness of the Moon Using the Wavelet Leaders Method and the Lunar Digital Elevation Model From the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera

Contact Info

Product

Resources

About